- Organizational meeting
- Probability that random polynomial has no real roots (Talk by Anna Gusakova)
- Theorems on positive real functions (Talk by Anna Muranova)
- Non-explosion of solutions to SDEs with singular coefficients (Talk by Chengcheng Ling)
- Emergence of Flocking in the Fractional Cucker-Smale Model (Talk by Peter Kuchling)

- Introduction to partition functions
- Partition Functions and Gibbs Measures
- Correlation Functions
- Phase Transitions (Critical Exponents and Models)
- Scaling Limits

**Reading** *Spectral graph theory* by Fan R. K. Chung

- Chapter 2: Isoperimetric problems
- Chapter 3: Diameters and eigenvalues
- Talk by Anna Muranova: On effective resistance of electric network with impedances
- Talk by Melissa Meinert: Ollivier Ricci curvature for general Laplacians
- Markov chains
- Talk by Filip Bosnic: Examples of Poincaré and log-Sobolev inequalities on discrete configuration spaces
- Introduction to random graphs by Alan Frieze and Michał Karoński

**Discuss** *Lévy Processes and Infinitely Divisible Distributions* by Ken-iti Sato

- Chapter 1 (pp. 1 - 30): Examples of Levy Processes

- Chapter 2 (pp. 31 - 68): Characterisation and Existence of Levy Processes and Additive Processes
- Chapter 2 (pp. 31 - 41): Infinitely Divisible Processes and the Lévy-Khintchine formula
- Chapter 2 (pp. 54 - 67): Transition Functions and the Markov Property; Existence of Lévy and Additive Processes
- Chapter 3 (pp. 69 - 77): Selfsimilar and Semi-selfsimilar Processes and their Exponents
- Chapter 3 (pp. 77 - 90): Representations of Stable and Semi-stable Distributions
- Viswanathan et al. Papers: “Levy Flight Search Patterns of Wandering Albatrosses” and “Optimizing the Success of Random Searches”
- Bertoin (pp. 18-24): Potential theory: Markov property and important definitions
- Bertoin (pp. 43-48): Duality and time reversal
- Bertoin (pp. 48-56): Potential theory: capacity measure; essentially polar sets and capacity
- Bertoin (pp. 56-68): Potential theory: energy; the case of a single point
- Bertoin (pp. 71-84): Subordinators: definitions; passage across a level; arcsine laws
- Bertoin (pp. 84-99): Subordinators: rates of growth; (Hausdorff-)dimension of the range

**Discuss**

- Maximum principle for ecliptic operators (
*Gibarg-Trudinger*) - Paley-Littlewood Decomposition (
*Grafakos classical Fourrier Analysis, second or third edtion*) - Another looks at Sobolev spaces (
*Articles Brezis Bourgain_Mironescu*) - Spectral theory: spectral measure for Unbounded operators
- Spectral theory for unbounded operator and spectral measure (Book by Reed-Simon)
- Restriction of the Fourier Transform on the sphere (Book by Elias Stein)
- Interplation of Banach spaces and application (Lecture note by Alessandra Lunadri Theory of interpolation 2009)
- Introduction to optimal transport theory (Book by Cedri Villani: Old and New, it is free on-line)
- Introduction to control and non linearity (Book by Jean-Michel Coron: Control and Non-linearity free one his we-page)
- Introduction to Calculus of variations